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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



$ K$-groups generated by $ K$-spaces

Author: Eric C. Nummela
Journal: Trans. Amer. Math. Soc. 201 (1975), 279-289
MSC: Primary 22A05; Secondary 20E05
MathSciNet review: 0352319
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Abstract: A $ K$-group $ G$ with identity $ e$ is said to be generated by the $ K$-space $ X$ if $ X$ is a subspace of $ G$ containing $ e,X$ algebraically generates $ G$, and the canonical morphism from the Graev free $ K$-group over $ (X,e)$ on-to $ G$ is a quotient morphism. An internal characterization of the topology of such a group $ G$ is obtained, as well as a sufficient condition that a subgroup $ H$ of $ G$ be generated by a subspace $ Y$ of $ H$. Several illuminating examples are provided.

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Keywords: $ K$-space, $ K$-group, free group
Article copyright: © Copyright 1975 American Mathematical Society